Dice pls help need answer

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on any roll of a set of two fair 12 sided dice, the probability of obtaining a product that is an even number or a product of greater than 30, adds to a number larger than 1. Given we know the probability of an event must lie between 0 and 1 explain in your own words if this is possible

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What do you think about it? We want to work with you, helping you to think through it on your own, and for that, we need to know where you are coming from. (And don't forget that "in your own words" means your words, not ours! This is meant to be a chance for you to think for yourself, not just to get someone else to think.)

Elite Member

on any roll of a set of two fair 12 sided dice, the probability of obtaining a product that is an even number or a product of greater than 30, adds to a number larger than 1. Given we know the probability of an event must lie between 0 and 1 explain in your own words if this is possible

Elite Member

on any roll of a set of two fair 12 sided dice, the probability of obtaining a product that is an even number or a product of greater than 30, adds to a number larger than 1. Given we know the probability of an event must lie between 0 and 1 explain in your own words if this is possible

I think there maybe a translation problem here. Taking what is posted verbatim, twelve sided dice numbered \(\displaystyle 1\text{ to 12}\) and product (not sum) of the faces. There are \(\displaystyle 144\) possible pairs of which we want to count any pair which has a product which is even or has value greater than thirty. Any pair with an even number yields an even product. Thus remove any pair that contains two odd numbers whose product is less than thirty. That count is \(\displaystyle \|(\{1,3,5\}\times\{1,3,5\}\cup\{(1,7)\,(7,1)\,(1,9)\,(9,1)\,(3,7)\,(7,3)\,(1,11)\,(11,1)\}\|=17\) OR \(\displaystyle 144-17=127\) pairs the product of which is even or less than thirty. Thus what the is probability of obtaining a product that is an even number or a product of greater than 30 ?

Elite Member

on any roll of a set of two fair 12 sided dice, the probability of obtaining a product that is an even number or a product of greater than 30, adds to a number larger than 1. Given we know the probability of an event must lie between 0 and 1 explain in your own words if this is possible

It says, if you do a calculation of the probability by adding some numbers (a common mistake in an "or" probability problem), and the result is greater than 1, what can you say about your answer, and why? It's a true/false question, with explanation.

I suppose I could be wrong; I'm taking the last phrase to mean "explain whether this can be correct", whereas literally it could be taken as "explain (if you are able to)."

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Elite Member

We need to figure out what the problem is really asking. I just stated my interpretation; do you think I am right?

As I read it, the answer is merely: "The answer you got, which is greater than 1, can't be correct, because probabilities can't be greater than 1." I think that's all they want.

Or, as I hinted earlier, you could explain specifically why the method, not just the answer, is wrong: You can't just add two probabilities, because the formula for "or" is

P(A or B) = P(A) + P(B) - P(A and B)​

The two events overlap, so you have to subtract that overlap, which will bring the answer down below 1. That is, in adding, you will have counted even numbers greater than 30 twice.

On the other hand, if you think it is asking for the probability, you can either do what pka showed (which I imagine may be written in a style a bit over your head), or just make a table showing all 144 possible products, mark those which are either even or greater than 30, and count them. You should get the number pka gave (assuming he didn't miss anything). Then put that over 144, and you have the answer.

I dislike questions that are as hard to interpret as this one is; they lead to unnecessary frustration, often over very simple problems.

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Super Moderator

I thought, when I initially read the problem, that the student was supposed to determine why we cannot simply add the separate probabilities to get the composite probability, namely because the two events are not independent.

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This is not possible as the formula for probabilities is P(A or B) = P(A) + P(B) - P(A and B) and you can't add separate probabilities because the two events are not independent, probabilities also cannot be above one. is that correct?

New member

This is not possible as the formula for probabilities is P(A or B) = P(A) + P(B) - P(A and B) and you can't add separate probabilities because the two events are not independent, probabilities also cannot be above one. is that correct?